Water Flow at the Local (Formation) Scale

Abstract

Beginning with the present part, and in the rest of this book, we shall study flow and transport in natural porous formations. These formations differ considerably from the laboratory samples (considered in Part 2) in a few respects, but mainly in their dimensions. Thus, natural formations, or aquifers, appear generally as predominantly horizontal layers whose thickness may vary between a few to hundreds of meters. Their planar extent is generally much larger than the thickness, the horizontal size being as large as tens of kilometers. At these vast scales, as compared to the porescale, the properties and flow variables of interest are the macroscopic ones discussed in Part 2. In other words, measurements or computations are carried out for variables averaged over volumes or surfaces which are large enough to warrant the use of macroscopic quantities regarded as deterministic and attached to each point in space, in the spirit of the discussion of Chap. 2.1. The heterogeneity at pore-scale is, therefore, ignored and its presence manifests indirectly in the equations satisfied by macroscopic variables and in the coefficients (permeability, effective storativity, etc) which characterize the macroscopic properties of the porous medium. Along these lines, the porous medium and the fluid are regarded as continua and the macroscopic properties and variables are represented mathematically as continuous spatial scalar, vector or tensor fields. To illustrate the concept, let us consider the meaning of permeability k at a point x: it is the one of a core surrounding the point, which is hypothetically or actually extracted from the formation and brought to the laboratory for measurement.